Example of a non-log-concave Duistermaat-Heckman measure
نویسندگان
چکیده
منابع مشابه
Example of a Non-log-concave Duistermaat-heckman Measure
We construct a compact symplectic manifold with a Hamiltonian circle action for which the Duistermaat-Heckman function is not log-concave.
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Karshon constructed the first counterexample to the log-concavity conjecture for the Duistermaat-Heckman measure: a Hamiltonian six manifold whose fixed points set is the disjoint union of two copies of T. In this article, for any closed symplectic four manifold N with b > 1, we show that there is a Hamiltonian circle manifold M fibred over N such that its DuistermaatHeckman function is not log...
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Lutian Zhao UID: 661622198 The Duistermaat-Heckman theorems concern the measure associated to moment map of a torus action of symplectic manifold. Typically, this name refers to two theorems, one is called the ”Duistermaat-Heckman measure", which says that ”the Radon-Nikodym derivative is piecewise polynomial", the definition of each terms will be introduced later. The second one is called ”Dui...
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We prove a Duistermaat-Heckman type formula in a suitable non-compact setting. We use this formula to evaluate explicitly the pushforward of the Liouville measure via the moment map of both an abelian and a non-abelian group action. As an application we obtain the classical analogues of well-known multiplicity formulas for the holomorphic discrete series representations.
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Here we develop an explicitly covariant expression for the stationary phase approximation of a classical partition function based on geometric properties of the phase space. As an example of the utility of such an evaluation we show that in the case of the Hamiltonian ows generating conformal rescalings of the underlying geometry, the classical partition function is given exactly by the leading...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 1996
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.1996.v3.n4.a11